Skew-product systems over infinite interval exchange transformations

Abstract

We study the ergodic properties (recurrence, discrepancy, diffusion coefficients and ergodicity itself) of a class of $\mathbb{Z}$-extensions over infinite interval exchange transformations called rotated odometers. The choice of a skew-function is motivated by the use in the study of parallel flows on a particular staircase manifold of infinite genus.

37 pages. New section added (section 2), which explains the relation between the skew-products considered in the paper, and the first return maps of flows on translation surfaces